Question

You just received a bonus of 1,000.

a.  Calculate the future value of 1,000​, given that it will be held in the bank for 8 years and earn an annual interest rate of 4 percent.

b.  Recalculate part (a​) using a compounding period that is​ (1) semiannual and​ (2) bimonthly.

c.  Recalculate parts (a​) and (b​) using an annual interest rate of 8 percent.

d.  Recalculate part (a​) using a time horizon of 16 years at an annual interest rate of 4 percent.

e.  What conclusions can you draw when you compare the answers in parts (c​) and (d​) with the answers in parts (a​) and (b​)?

Answer 1

Here, in these questions, we willl use the formula for Future value:

FV = PV * (1+r%)ⁿ

where, FV = future value, PV= Present value, R= rate of interest, n = time period.

(a) PV = $1000, n= 8, r= 4% (annual compounding)

FV = 1000 * (1+.04)⁸

FV = 1000 * (1.04)⁸

FV= $1368.56

b) PV = $1000, n = 8 years, r = 4% (semi-annual compounding)

In semi annual compounding, r will be 4%/ 2 = 2% and n= 8*2 = 16

FV = 1000 * (1 + 2%)¹⁶

FV = 1000 * (1.02)¹⁶

FV = $1372.78

In bimonthly, compounding will be done twice in one month

PV = $1000, n = 8 years, r = 4% (bimonthly compounding - twice in 1 month)

bimonthly compounding, r = 4% / 24 and n= 8*24 = 192

FV = 1000 * (1 + 4%/24)¹⁹²

FV = $1376.76

(c) Annual rate = 8%

PV = $1000, n= 8, r= 8% (annual compunding)

FV = 1000 * (1+.08)⁸

FV = 1000 * (1.08)⁸

FV= $1850.93

PV = $1000, n = 8 years, r = 8% (semi-annual compounding)

In semi annual compounding, r will be 8%/ 2 = 4% and n= 8*2 = 16

FV = 1000 * (1 + 4%)¹⁶

FV = 1000 * (1.04)¹⁶

FV = $1872.98

In bimonthly, compounding will be done twice in one month

PV = $1000, n = 8 years, r = 8% (bimonthly compounding - twice in 1 month)

bimonthly compounding, r = 8% / 24 and n= 8*24 = 192

FV = 1000 * (1 + 8%/24)¹⁹²

FV = $1894.96

(d)  PV = $1000, n= 16, r= 4% (annual compounding)

FV = 1000 * (1+.04)¹⁶

FV = 1000 * (1.04)¹⁶

FV= $1872.98